How do you approach the management of amblyopia in children with developmental delays or cognitive impairments?

I agree with Dr. @Dr. First Last!

We never want to not offer the best therapies to children due to a perceived developmental delay or cognitive impairment. Many times, families and patients will surprise us and do wonderfully.

That being said, trying to understand the emotions of the family can be ...

Would approach the same way - start with patching or atropine. You might need to adjust times of day the family is patching in order to not interfere with therapies and other important activities of the day.